Krylov subspace methods based quaternion tensor form for generalized Sylvester quaternion tensor equation with application to color video restoration

Abstract

In this paper, we consider Krylov subspace methods based quaternion tensor form for a class of generalized Sylvester quaternion tensor equation. A novel quaternion tensor product and a global quaternion Arnoldi process based on the tensor form are proposed. Then, the quaternion tensor Krylov subspaces and their orthogonal bases are constructed via the proposed global quaternion Arnoldi process. The quaternion full orthogonalization method based on tensor format (denoted by QFOM−BTF) and the quaternion generalized minimal residual method based on tensor format (denoted by QGMRES−BTF) are established to solve the quaternion tensor equation. The theoretically analyze results of the proposals are discussed on the quaternion tensor form. Finally, we demonstrate the feasibility of QFOM−BTF and QGMRES−BTF methods on some numerical examples including the color video restoration.